The document discusses ratios, rates, and speed. It defines a ratio as a comparison of two similar quantities expressed as a fraction, and defines rate as a ratio with different units that can be simplified to a single unit. It provides examples of calculating ratios, unit rates, and average speed using the formulas speed=distance/time and average speed=total distance/total time.

3. 1. express comparison of quantities using ratio
2. express ratio in simplest form
3. solve for rate / speed

5. A is a comparison of two similar
quantities.
Given any two similar quantities, a and b, the ratio of a and b is
defined as
𝑎 ∶ 𝑏 =
𝑎
𝑏
𝑤ℎ𝑒𝑟𝑒 𝑏 ≠ 0
and a and b are called the of the ratio.

6. A is a comparison of
two similar quantities.
Example 1:
There are 10 boys and 30 girls in the Drama
Club. Find the ratio of:
a. the number of boys to the number of girls.
b. the number of girls to the total number of
members in the club.

7. A is a comparison of
two similar quantities.
Example 2:
It took Aaron 50 seconds to finish the entrance
examination. The same examination took Carl 2
minutes to finish. Find the ratio of Carl’s time to
Aaron’s time.

8. A is a comparison of
two similar quantities.
Example 3:
In a given farm there are:
10 chickens 5 sheeps 3 cows
Find the ratio of:
a. chickens to sheeps
b. chickens to cows
c. sheeps to cows
d. sheeps to chickens

9. question
s?

11. A is a ratio of two measurements
having different units of measurements.
When rate is simplified so it has a
denominator of 1, it is called a .

12. A is a ratio of two measurements having different units of
measurements.
Example 1:
Jenny can encode 300 words in 5
minutes. Find the unit rate.

13. A is a ratio of two measurements having different units of
measurements.
Example 2:
Find the unit rate in each case.
a. A car travelled 150 kilometers in 2 hours.
b. A car travels 264 kilometers and uses 28 liters
of gasoline.
c. An electrician took 4 hours to complete a job.
He charged P200 for his service.
d. Sam read 500 pages in 20 minutes.

14. question
s?

16. is used for the rate of change of
distance travelled.
𝑆𝑝𝑒𝑒𝑑 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑝𝑒𝑒𝑑 =
𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

17. is used for the rate of
change of distance travelled.
𝑆𝑝𝑒𝑒𝑑 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
Example 1:
A man jogs 1500 meters in 5
minutes. Find his speed.
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑝𝑒𝑒𝑑 =
𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

18. is used for the rate of
change of distance travelled.
𝑆𝑝𝑒𝑒𝑑 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
Example 2:
The average speed of a car for the
first 3 hours is 70kph. Its average speed
for the next 2 hours is 80kph. Find its
average speed.
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑝𝑒𝑒𝑑 =
𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

19. is used for the rate of
change of distance travelled.
𝑆𝑝𝑒𝑒𝑑 =
𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
Example 3:
They took 3 hours to drive from
Town A to Town B at an average speed of
40 km/h. Find the distance between town
A to town B.
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑆𝑝𝑒𝑒𝑑 =
𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑
𝑇𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛

20. question
s?